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Periodica Mathematica Hungarica, 1985
A graph is randomly matchable if every matching of the graph is contained in a perfect matching. We generalize this notion and say that a graph G is randomly H-coverable if every set of independent subgraphs, each isomorphic to H, that does not cover the vertices of G can be extended to a larger set of independent copies of H.
Fink, J. +3 more
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A graph is randomly matchable if every matching of the graph is contained in a perfect matching. We generalize this notion and say that a graph G is randomly H-coverable if every set of independent subgraphs, each isomorphic to H, that does not cover the vertices of G can be extended to a larger set of independent copies of H.
Fink, J. +3 more
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Combinatorics, Probability and Computing, 1997
In this note we give a probabilistic proof of the existence of an n-vertex graph Gn, n=1, 2, [ctdot ], such that, for some constant c>0, the edges of Gn cannot be covered by n−c log n complete bipartite subgraphs of Gn. This result improves a previous bound due to F. R. K. Chung and is the best possible up to a constant.
Rödl, Vojtěch, Ruciński, Andrzej
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In this note we give a probabilistic proof of the existence of an n-vertex graph Gn, n=1, 2, [ctdot ], such that, for some constant c>0, the edges of Gn cannot be covered by n−c log n complete bipartite subgraphs of Gn. This result improves a previous bound due to F. R. K. Chung and is the best possible up to a constant.
Rödl, Vojtěch, Ruciński, Andrzej
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Canadian Journal of Mathematics, 1958
For the purpose of analysing bipartite graphs (hereinafter called simply graphs) the concept of an exterior covering is introduced. In terms of this concept it is possible in a natural way to decompose any graph into two parts, an inadmissible part and a core.
Dulmage, A. L., Mendelsohn, N. S.
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For the purpose of analysing bipartite graphs (hereinafter called simply graphs) the concept of an exterior covering is introduced. In terms of this concept it is possible in a natural way to decompose any graph into two parts, an inadmissible part and a core.
Dulmage, A. L., Mendelsohn, N. S.
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SIAM Journal on Discrete Mathematics, 1992
Let \(G\) be a bridgeless graph with \(n\) vertices and \(m\) edges and let \(r\) be the minimum length of an even cycle in \(G\) of length at least 6 \((r=\infty\) if there is no such cycle). It is proved that the edges of \(G\) can be covered by cycles whose total length is at most \(m+(n-1)r/(r- 1)\).
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Let \(G\) be a bridgeless graph with \(n\) vertices and \(m\) edges and let \(r\) be the minimum length of an even cycle in \(G\) of length at least 6 \((r=\infty\) if there is no such cycle). It is proved that the edges of \(G\) can be covered by cycles whose total length is at most \(m+(n-1)r/(r- 1)\).
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Mathematics in Computer Science, 2009
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Acta Mathematica Scientia, 1989
Summary: A graph G is k-covered if each edge of G belongs to a k-factor of G. We determine some values of k for which every regular graph with edge- connectivity \(\lambda\) is k-covered.
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Summary: A graph G is k-covered if each edge of G belongs to a k-factor of G. We determine some values of k for which every regular graph with edge- connectivity \(\lambda\) is k-covered.
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Homological Coverings of Graphs
Journal of the London Mathematical Society, 1984The homology group of a graph, with any coefficient ring, can be used to construct covering graphs. The properties of the covering graph are studied, and it, is proved that they admit group of automorphisms related to the group of the base graph. In the case of cubic graphs the construction throws some light on classification problems and it can be ...
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